The present invention relates to the magnetic resonance art. It finds particular application in conjunction with Fourier transform imaging and will be described with particular reference thereto. It is to be appreciated, however, that the present invention may also find application in other imaging and spectroscopy techniques in which only a partial or incomplete data set is available.
Heretofore, medical diagnostic magnetic resonance imaging has included the sequential pulsing of radio frequency signals and magnetic field gradients across a region to be imaged. In two dimensional imaging, a patient is disposed in a region of interest in a substantially uniform main magnetic field. An RF excitation pulse is applied as a slice select gradient is applied across the field to select a slice or other region of the patient to be imaged. A phase encode gradient is applied along one of the axes of the selected slice to encode material with a selected phase encoding. In each repetition of the pulse sequence, the phase encode gradient is stepped in regular intervals from a negative maximum phase encode gradient through a zero phase encode gradient to a positive maximum phase encode gradient. Theoretically, the pair of views corresponding to positive and negative phase encode gradients have a symmetric relationship. However, in practice the symmetry relationship is rendered unpredictable by sequence and field dependent phase considerations. In order to overcome these difficulties, conventionally both positive and negative phase encode views are collected in order to form a phase independent magnitude image.
Magnetization manipulation pulses are applied to cause a magnetic resonance echo. During the echo following each pulse sequence, one set of data points, generally termed a view or step, is sampled. The data points within each view correspond to a preselected range of frequencies f.sub.o .+-..DELTA.f, where f.sub.o is the frequency of the center data value of the view. For the zero phase encoding view, a datum frequency f.sub.o +.DELTA.f.sub.1 is related to that of f.sub.o -.DELTA.f.sub.1. The data values for a positive phase encode view corresponding to a frequency f.sub.o +.DELTA.f.sub.1 are also related to the corresponding negative phase encode view at frequency f.sub.o -.DELTA.f.sub.1 by conjugate symmetry. In this manner, each data point in a full data set, sometimes referred to as k space, is related to another point by the underlying property of conjugate symmetry. The complete set of views is operated on by a two dimensional inverse Fourier transform to derive an image representation.
Others have reconstructed images utilizing only half a set of views, i.e. only the positive views or only the negative views. In one such half data reconstruction, about eight additional views were collected adjacent the zero or minimum phase encoding. The sixteen central views about the zero phase encoding were utilized to derive a phase map. The acquired data was filtered and the data set was completed by filling with zeros. The Fourier transform of this data set was then phase corrected by the phase map to yield the final reconstruction. However, this technique produced less than satisfactory images which were particularly sensitive to artifacts caused by motioninduced errors in phase.
The present invention provides a new and improved technique for reconstructing images with less than a full set of data.